If $a, c, d$ are in A.P., then $r_{1}, r_{2}, r_{3}$ are in

A . P

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G . P

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H . P

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n o n e

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Solution

The correct option is C $H . P$
As $r_{1} = \frac{△}{S - a}, r_{2} = \frac{△}{S - b}, r_{3} = \frac{△}{S - c}$
$\Rightarrow \frac{1}{r_{1}} = \frac{c}{△} - \frac{a}{△}, \frac{1}{r_{2}} = \frac{s}{△} - \frac{b}{△}, \frac{1}{r_{3}} = \frac{s}{△} - \frac{c}{△}$
As a, b, c are in A.p.
$\Rightarrow \frac{1}{r_{1}}, \frac{1}{r_{2}}, \frac{1}{r_{3}}$ are in A.P
$\Rightarrow r_{1}, r_{2}, r_{3}$ are in H.P $\Rightarrow (c)$

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Similar questions

If the sides fo a triangle are in A.P. as well as in G.P. Then the value of $\frac{r_{1}}{r_{2}} - \frac{r_{2}}{r_{3}}$

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